Colored Voronoi Diagram: Partitioning the Plane by Seed Points

This example demonstrates a colored Voronoi diagram: given a finite set of seed points, the plane is partitioned into regions where each point in a region is closer (under the chosen distance measure) to its corresponding seed than to any other seed. The key math concepts are Voronoi tessellation, distance-based region boundaries, and the fact that Voronoi edges are loci of points equidistant to two (or more) seeds. Construction-wise, GeoGebra uses the Voronoi command to compute the partition, while Sequence and Element are used to organize the discrete set of sites and select/manage the resulting geometric objects. From the provided construct summary, objects such as T, S, R, Q, P, O, …, A (plus graphe1, l1, and collections like A1–A17) act as seeds/auxiliary parameters and display targets, enabling the colored visualization of different cells. Suitable for high school to early university use, for teaching computational geometry ideas, algorithmic visualization, and geometric construction practice.